{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Maze Solver\n",
    "In this notebook, we write a maze solver by solving the Poisson equation with two Dirichlet boundary conditions imposed on the two faces that correspond to the start and end of the maze, respectively. \n",
    "\n",
    "The logic is pretty simple: once we have the solution, we just need to start off from one face and follow the gradient. Since the gradient in the deadends is almost close to 0, following the nonzero gradient should guide us toward the other side of the maze.\n",
    "\n",
    "We implement two different approaches:\n",
    "\n",
    "1. Direct numerical simulation\n",
    "Here, we first convert the image into a Cubic network, trim the pores that correspond to the walls, and finally run a basic `OhmicConduction` (or `FickianDiffusion`) on the resulting trimmed network.\n",
    "\n",
    "2. Network extraction\n",
    "Here, we first use the SNOW algorithm to extract the equivalent network of the maze. Note that the nodes in the equivalent network will not exactly give us the corners of the maze, but at least it gives us a rough idea, enough for solving the maze! Then, like the first approach, we run a basic `OhmicConduction` on the extracted network. The advantage of this approach is that it's way faster due to much fewer unknowns.\n",
    "\n",
    "Note: Inspired by this post by Jeremy Theler https://www.linkedin.com/posts/jeremytheler_how-to-solve-a-maze-without-ai-use-laplaces-activity-6831291311832760320-x9d5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Install the required pmeal packages in the current Jupyter kernel\n",
    "import sys\n",
    "try:\n",
    "    import openpnm as op\n",
    "except:\n",
    "    !{sys.executable} -m pip install openpnm\n",
    "    import openpnm as op\n",
    "try:\n",
    "    import porespy as ps\n",
    "except:\n",
    "    !{sys.executable} -m pip install porespy\n",
    "    import porespy as ps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import requests\n",
    "import numpy as np\n",
    "from scipy import ndimage\n",
    "import matplotlib.pyplot as plt\n",
    "import porespy as ps\n",
    "import openpnm as op\n",
    "from openpnm.utils import tic, toc\n",
    "from PIL import Image\n",
    "from io import BytesIO\n",
    "%config InlineBackend.figure_formats = ['svg']\n",
    "ws = op.Workspace()\n",
    "ws.settings[\"loglevel\"] = 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load maze samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "im_size = 'medium'\n",
    "\n",
    "if im_size == 'small':\n",
    "    url = 'https://imgur.com/ZLbV4eh.png'\n",
    "elif im_size == 'medium':\n",
    "    url = 'https://imgur.com/A3Jx8SJ.png'\n",
    "else:\n",
    "    url = 'https://imgur.com/FLJ21e5.png'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "    <dc:date>2021-09-13T10:34:49.599892</dc:date>\r\n",
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       "   </g>\r\n",
       "  </g>\r\n",
       " </g>\r\n",
       " <defs>\r\n",
       "  <clipPath id=\"p5f19c8a10d\">\r\n",
       "   <rect height=\"271.8\" width=\"271.8\" x=\"7.2\" y=\"7.2\"/>\r\n",
       "  </clipPath>\r\n",
       " </defs>\r\n",
       "</svg>\r\n"
      ],
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "response = requests.get(url)\n",
    "img = Image.open(BytesIO(response.content))\n",
    "im = np.array(img.getdata()).reshape(img.size[0], img.size[1], 4)[:, :, 0]\n",
    "im = im == 255\n",
    "\n",
    "Nx, Ny, = im.shape\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(5, 5))\n",
    "ax.imshow(im, cmap='Blues', interpolation=\"none\")\n",
    "ax.axis(\"off\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Approach A: Direct numerical simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Thicken the walls to reduce number of unknowns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Structuring element for thickening walls\n",
    "strel = np.array([[1, 1, 1],\n",
    "                  [1, 1, 1],\n",
    "                  [1, 1, 1]])\n",
    "\n",
    "# Save some computation by thickening the walls\n",
    "def thicken_wall(im):\n",
    "    return ~ndimage.morphology.binary_dilation(~im, structure=strel)\n",
    "\n",
    "for _ in range(5):\n",
    "    im = thicken_wall(im)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.5, 801.5, 801.5, -0.5)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/svg+xml": [
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       "<svg height=\"286.2pt\" version=\"1.1\" viewBox=\"0 0 286.2 286.2\" width=\"286.2pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\r\n",
       " <metadata>\r\n",
       "  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\r\n",
       "   <cc:Work>\r\n",
       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\r\n",
       "    <dc:date>2021-09-13T10:34:52.486279</dc:date>\r\n",
       "    <dc:format>image/svg+xml</dc:format>\r\n",
       "    <dc:creator>\r\n",
       "     <cc:Agent>\r\n",
       "      <dc:title>Matplotlib v3.4.1, https://matplotlib.org/</dc:title>\r\n",
       "     </cc:Agent>\r\n",
       "    </dc:creator>\r\n",
       "   </cc:Work>\r\n",
       "  </rdf:RDF>\r\n",
       " </metadata>\r\n",
       " <defs>\r\n",
       "  <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\r\n",
       " </defs>\r\n",
       " <g id=\"figure_1\">\r\n",
       "  <g id=\"patch_1\">\r\n",
       "   <path d=\"M 0 286.2 \r\n",
       "L 286.2 286.2 \r\n",
       "L 286.2 0 \r\n",
       "L 0 0 \r\n",
       "z\r\n",
       "\" style=\"fill:none;\"/>\r\n",
       "  </g>\r\n",
       "  <g id=\"axes_1\">\r\n",
       "   <g clip-path=\"url(#p8a5160f946)\">\r\n",
       "    <image height=\"802\" id=\"image20ff3a052f\" style=\"image-rendering:crisp-edges;image-rendering:pixelated\" transform=\"matrix(0.339152 0 0 0.339152 7.2 7)\" width=\"802\" xlink:href=\"data:image/png;base64,\r\n",
       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       "   </g>\r\n",
       "  </g>\r\n",
       " </g>\r\n",
       " <defs>\r\n",
       "  <clipPath id=\"p8a5160f946\">\r\n",
       "   <rect height=\"271.8\" width=\"271.8\" x=\"7.2\" y=\"7.2\"/>\r\n",
       "  </clipPath>\r\n",
       " </defs>\r\n",
       "</svg>\r\n"
      ],
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(5, 5))\n",
    "ax.imshow(im, cmap='Blues', interpolation=\"none\")\n",
    "ax.axis(\"off\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convert the maze into a Cubic network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get top and bottom boundaries\n",
    "BP_top = np.zeros_like(im)\n",
    "BP_bot = np.zeros_like(im)\n",
    "BP_top[0, :] = True\n",
    "BP_bot[-1, :] = True\n",
    "BP_top *= im\n",
    "BP_bot *= im\n",
    "\n",
    "# Make a cubis network with same dimensions as image and assign the props\n",
    "net = op.network.Cubic(shape=[Nx, Ny, 1])\n",
    "net['pore.index'] = np.arange(0, net.Np)\n",
    "net['pore.BP_top'] = BP_top.flatten()\n",
    "net['pore.BP_bot'] = BP_bot.flatten()\n",
    "\n",
    "# Trim wall pores\n",
    "op.topotools.trim(network=net, pores=~im.flatten())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solve the Poisson equation ($\\nabla^2 \\phi = 0$) on the maze"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solve time: 0.567 s\n"
     ]
    }
   ],
   "source": [
    "# Set up a dummy phase and apply uniform arbitrary conductance\n",
    "phase = op.phases.GenericPhase(network=net)\n",
    "phase['throat.electrical_conductance'] = 1.0\n",
    "\n",
    "# Run algorithm\n",
    "alg = op.algorithms.OhmicConduction(network=net, phase=phase)\n",
    "alg.set_value_BC(pores=net.pores('BP_top'), values=0.0)\n",
    "alg.set_value_BC(pores=net.pores('BP_bot'), values=1.0)\n",
    "tic()\n",
    "alg.run()\n",
    "dt = toc(quiet=True);\n",
    "print(f'Solve time: {dt:.3f} s')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Follow the gradient!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\r\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\r\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\r\n",
       "<svg height=\"286.2pt\" version=\"1.1\" viewBox=\"0 0 286.2 286.2\" width=\"286.2pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\r\n",
       " <metadata>\r\n",
       "  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\r\n",
       "   <cc:Work>\r\n",
       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\r\n",
       "    <dc:date>2021-09-13T10:34:56.264927</dc:date>\r\n",
       "    <dc:format>image/svg+xml</dc:format>\r\n",
       "    <dc:creator>\r\n",
       "     <cc:Agent>\r\n",
       "      <dc:title>Matplotlib v3.4.1, https://matplotlib.org/</dc:title>\r\n",
       "     </cc:Agent>\r\n",
       "    </dc:creator>\r\n",
       "   </cc:Work>\r\n",
       "  </rdf:RDF>\r\n",
       " </metadata>\r\n",
       " <defs>\r\n",
       "  <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\r\n",
       " </defs>\r\n",
       " <g id=\"figure_1\">\r\n",
       "  <g id=\"patch_1\">\r\n",
       "   <path d=\"M 0 286.2 \r\n",
       "L 286.2 286.2 \r\n",
       "L 286.2 0 \r\n",
       "L 0 0 \r\n",
       "z\r\n",
       "\" style=\"fill:none;\"/>\r\n",
       "  </g>\r\n",
       "  <g id=\"axes_1\">\r\n",
       "   <g clip-path=\"url(#p853916d90b)\">\r\n",
       "    <image height=\"802\" id=\"image2213fd05b3\" style=\"image-rendering:crisp-edges;image-rendering:pixelated\" transform=\"matrix(0.339152 0 0 0.339152 7.2 7)\" width=\"802\" xlink:href=\"data:image/png;base64,\r\n",
       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\"/>\r\n",
       "   </g>\r\n",
       "  </g>\r\n",
       " </g>\r\n",
       " <defs>\r\n",
       "  <clipPath id=\"p853916d90b\">\r\n",
       "   <rect height=\"271.8\" width=\"271.8\" x=\"7.2\" y=\"7.2\"/>\r\n",
       "  </clipPath>\r\n",
       " </defs>\r\n",
       "</svg>\r\n"
      ],
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculate flux in throats and show in pores\n",
    "# Note: No need to calculate pore.rate as it auto interpolates from throat values\n",
    "phase['throat.rate'] = alg.rate(throats=net.Ts, mode='single')\n",
    "rate_im = np.ones([Nx, Ny]).flatten() * np.nan\n",
    "rate_im[net['pore.index']] = phase['pore.rate']\n",
    "rate_im = rate_im.reshape([Nx, Ny])\n",
    "\n",
    "# Plot the maze solution\n",
    "fig, ax = plt.subplots(figsize=(5, 5))\n",
    "ax.imshow(rate_im, cmap='jet', interpolation=\"none\")\n",
    "ax.axis(\"off\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Approach B: Network extraction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Network extraction using SNOW algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Extracting pore and throat properties:   0%|          | 0/1488 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We need to pass image transpose since matrix xy coords is inverted\n",
    "# i.e., row is x and col is y, whereas in Cartesian convention, it's the opposite.\n",
    "out = ps.networks.snow2(im.T) \n",
    "proj = op.io.PoreSpy.import_data(out.network)\n",
    "net = proj.network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solve the Poisson equation ($\\nabla^2 \\phi = 0$) on the extracted network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solve time: 0.013 s\n"
     ]
    }
   ],
   "source": [
    "# Set up a dummy phase and apply uniform arbitrary conductance\n",
    "phase = op.phases.GenericPhase(network=net)\n",
    "phase['throat.electrical_conductance'] = 1.0\n",
    "\n",
    "# Run algorithm\n",
    "alg = op.algorithms.OhmicConduction(network=net, phase=phase)\n",
    "alg.set_value_BC(pores=net.pores('ymin'), values=0.0)\n",
    "alg.set_value_BC(pores=net.pores('ymax'), values=1.0)\n",
    "tic()\n",
    "alg.run()\n",
    "dt = toc(quiet=True);\n",
    "print(f'Solve time: {dt:.3f} s')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Follow the gradient!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\r\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\r\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\r\n",
       "<svg height=\"321.8pt\" version=\"1.1\" viewBox=\"0 0 312.925 321.8\" width=\"312.925pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\r\n",
       " <metadata>\r\n",
       "  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\r\n",
       "   <cc:Work>\r\n",
       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\r\n",
       "    <dc:date>2021-09-13T10:35:03.123913</dc:date>\r\n",
       "    <dc:format>image/svg+xml</dc:format>\r\n",
       "    <dc:creator>\r\n",
       "     <cc:Agent>\r\n",
       "      <dc:title>Matplotlib v3.4.1, https://matplotlib.org/</dc:title>\r\n",
       "     </cc:Agent>\r\n",
       "    </dc:creator>\r\n",
       "   </cc:Work>\r\n",
       "  </rdf:RDF>\r\n",
       " </metadata>\r\n",
       " <defs>\r\n",
       "  <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\r\n",
       " </defs>\r\n",
       " <g id=\"figure_1\">\r\n",
       "  <g id=\"patch_1\">\r\n",
       "   <path d=\"M 0 321.8 \r\n",
       "L 312.925 321.8 \r\n",
       "L 312.925 0 \r\n",
       "L 0 0 \r\n",
       "z\r\n",
       "\" style=\"fill:none;\"/>\r\n",
       "  </g>\r\n",
       "  <g id=\"axes_1\">\r\n",
       "   <g clip-path=\"url(#p8938083f9b)\">\r\n",
       "    <image height=\"802\" id=\"image51173f6c6a\" style=\"image-rendering:crisp-edges;image-rendering:pixelated\" transform=\"matrix(0.372818 0 0 0.372818 7.2 11.1625)\" width=\"802\" xlink:href=\"data:image/png;base64,\r\n",
       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      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
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     },
     "metadata": {
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   ],
   "source": [
    "# Get throat rate values\n",
    "phase['throat.rate'] = alg.rate(throats=net.Ts, mode='single')\n",
    "\n",
    "# Plot the maze solution (i.e., throat rates!)\n",
    "fig, ax = plt.subplots(figsize=(5, 5))\n",
    "op.topotools.plot_connections(net, ax=ax,\n",
    "                              color_by=phase[\"throat.rate\"],\n",
    "                              linewidth=2, cmap=\"Wistia\")\n",
    "ax.imshow(im, interpolation=\"none\", cmap='Blues');\n",
    "ax.axis(\"off\");"
   ]
  }
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